arXiv subjects

Michael Markl

Publications and source records attributed to Michael Markl.

14 recordsLinked to original sources

arXiv2025

Enabling Ultra-Fast Cardiovascular Imaging Across Heterogeneous Clinical Environments with A Generalist Foundation Model and Multimodal Database

Multimodal cardiovascular magnetic resonance (CMR) imaging provides comprehensive and non-invasive insights into cardiovascular disease (CVD) diagnosis and underlying mechanisms. Despite decades of advancements, its widespread clinical adoption remains constrained by prolonged scan times, inconsistent image quality, and heterogeneity across medical environments. This underscores the urgent need for a generalist reconstruction foundation model for ultra-fast CMR imaging, one formulated for physics-constrained inverse problems in the sensor (k-space) domain, capable of adapting across diverse imaging scenarios and serving as the essential substrate for all downstream analyses. To enable this goal, we curate MMCMR-427K, the largest and most comprehensive multimodal CMR k-space database to date, comprising 427,465 multi-coil k-space data paired with structured metadata across 13 international centers, 12 CMR modalities, 15 scanners spanning four field strengths, and 17 CVD categories in populations across three continents. Building on this unprecedented resource, we introduce CardioMM, a generalist reconstruction foundation model capable of dynamically adapting to heterogeneous fast CMR imaging scenarios. CardioMM unifies semantic contextual understanding with physics-informed data consistency to deliver robust reconstructions across varied scanners, protocols, and patient presentations. Comprehensive evaluations demonstrate that CardioMM achieves state-of-the-art performance across internal centers and exhibits strong zero-shot generalization to unseen external settings. Importantly, CardioMM supports acceleration up to 24x, providing the first evidence that such extreme acquisition speed can preserve key cardiac phenotypes, quantitative myocardial biomarkers, and diagnostic image quality without compromising clinical integrity.

eess.IV↗

arXiv2025

Automated Labeling of Intracranial Arteries with Uncertainty Quantification Using Deep Learning

Accurate anatomical labeling of intracranial arteries is essential for cerebrovascular diagnosis and hemodynamic analysis but remains time-consuming and subject to interoperator variability. We present a deep learning-based framework for automated artery labeling from 3D Time-of-Flight Magnetic Resonance Angiography (3D ToF-MRA) segmentations (n=35), incorporating uncertainty quantification to enhance interpretability and reliability. We evaluated three convolutional neural network architectures: (1) a UNet with residual encoder blocks, reflecting commonly used baselines in vascular labeling; (2) CS-Net, an attention-augmented UNet incorporating channel and spatial attention mechanisms for enhanced curvilinear structure recognition; and (3) nnUNet, a self-configuring framework that automates preprocessing, training, and architectural adaptation based on dataset characteristics. Among these, nnUNet achieved the highest labeling performance (average Dice score: 0.922; average surface distance: 0.387 mm), with improved robustness in anatomically complex vessels. To assess predictive confidence, we implemented test-time augmentation (TTA) and introduced a novel coordinate-guided strategy to reduce interpolation errors during augmented inference. The resulting uncertainty maps reliably indicated regions of anatomical ambiguity, pathological variation, or manual labeling inconsistency. We further validated clinical utility by comparing flow velocities derived from automated and manual labels in co-registered 4D Flow MRI datasets, observing close agreement with no statistically significant differences. Our framework offers a scalable, accurate, and uncertainty-aware solution for automated cerebrovascular labeling, supporting downstream hemodynamic analysis and facilitating clinical integration.

cs.CV↗

arXiv2025

Carbon Pricing in Traffic Networks

Traffic is a significant source of global carbon emissions. In this paper, we study how carbon pricing can be used to guide traffic towards equilibria that respect given emission budgets. In particular, we consider a general multi-commodity flow model with flow-dependent externalities. These externalities may represent carbon emissions, entering a priced area, or the traversal of paths regulated by tradable credit schemes. We provide a complete characterization of all flows that can be attained as Wardrop equilibria when assigning a single price to each externality. More precisely, we show that every externality budget achievable by any feasible flow in the network can also be achieved as a Wardrop equilibrium by setting appropriate prices. For extremal and Pareto-minimal budgets, we show that there are prices such that all equilibria respect the budgets. Although the proofs of existence of these particular prices rely on fixed-point arguments and are non-constructive, we show that in the case where the equilibrium minimizes a convex potential, the prices can be obtained as Lagrange multipliers of a suitable convex program. In the case of a single externality, we prove that the total externality caused by the traffic flow is decreasing in the price. For increasing, continuous, and piecewise affine travel time functions with a single externality, we give an output-polynomial algorithm that computes all equilibria implementable by pricing the externality. Even though there are networks where the output size is exponential in the input size, we show that the minimal price obeying a given budget can be computed in polynomial time. This allows the efficient computation of the market price of tradable credit schemes. Overall, our results show that carbon pricing is a viable and (under mild assumptions) tractable approach to achieve all feasible emission goals in traffic networks.

cs.GT↗

arXiv2025

Towards Modality- and Sampling-Universal Learning Strategies for Accelerating Cardiovascular Imaging: Summary of the CMRxRecon2024 Challenge

Cardiovascular health is vital to human well-being, and cardiac magnetic resonance (CMR) imaging is considered the {clinical reference standard} for diagnosing cardiovascular disease. However, its adoption is hindered by long scan times, complex contrasts, and inconsistent quality. While deep learning methods perform well on specific CMR imaging {sequences}, they often fail to generalize across modalities and sampling schemes. The lack of benchmarks for high-quality, fast CMR image reconstruction further limits technology comparison and adoption. The CMRxRecon2024 challenge, attracting over 200 teams from 18 countries, addressed these issues with two tasks: generalization to unseen {modalities} and robustness to diverse undersampling patterns. We introduced the largest public multi-{modality} CMR raw dataset, an open benchmarking platform, and shared code. Analysis of the best-performing solutions revealed that prompt-based adaptation and enhanced physics-driven consistency enabled strong cross-scenario performance. These findings establish principles for generalizable reconstruction models and advance clinically translatable AI in cardiovascular imaging.

eess.IV↗

arXiv2024

Stochastic Prediction Equilibrium for Dynamic Traffic Assignment

Stochastic effects significantly influence the dynamics of traffic flows. Many dynamic traffic assignment (DTA) models attempt to capture these effects by prescribing a specific ratio that determines how flow splits across different routes based on the routes' costs. Other models take a game-theoretic perspective and describe the equilibria resulting from the individual traffic participants' decisions instead of prescribing flow splits, however they usually neglect stochastic effects. In this paper, we propose a new unifying framework for DTA that incorporates the interplay between the routing decisions of each single traffic participant, the potentially stochastic nature of predicting the future state of the network, and the physical flow dynamics. Our framework consists of an edge loading operator modeling the physical flow propagation and a routing operator modeling the routing behavior of traffic participants. The routing operator is assumed to be set-valued and, thus, capable to model complex (deterministic) equilibrium conditions as well as stochastic equilibrium conditions assuming that measurements for predicting traffic are noisy. As our main results, we derive several quite general equilibrium existence and uniqueness results which not only subsume known results from the literature but also lead to new results. Specifically, for the new stochastic prediction equilibrium, we show existence and uniqueness under natural assumptions on the probability distribution over the predictions.

math.OC↗

arXiv2024

CMRxRecon2024: A Multi-Modality, Multi-View K-Space Dataset Boosting Universal Machine Learning for Accelerated Cardiac MRI

Cardiac magnetic resonance imaging (MRI) has emerged as a clinically gold-standard technique for diagnosing cardiac diseases, thanks to its ability to provide diverse information with multiple modalities and anatomical views. Accelerated cardiac MRI is highly expected to achieve time-efficient and patient-friendly imaging, and then advanced image reconstruction approaches are required to recover high-quality, clinically interpretable images from undersampled measurements. However, the lack of publicly available cardiac MRI k-space dataset in terms of both quantity and diversity has severely hindered substantial technological progress, particularly for data-driven artificial intelligence. Here, we provide a standardized, diverse, and high-quality CMRxRecon2024 dataset to facilitate the technical development, fair evaluation, and clinical transfer of cardiac MRI reconstruction approaches, towards promoting the universal frameworks that enable fast and robust reconstructions across different cardiac MRI protocols in clinical practice. To the best of our knowledge, the CMRxRecon2024 dataset is the largest and most protocal-diverse publicly available cardiac k-space dataset. It is acquired from 330 healthy volunteers, covering commonly used modalities, anatomical views, and acquisition trajectories in clinical cardiac MRI workflows. Besides, an open platform with tutorials, benchmarks, and data processing tools is provided to facilitate data usage, advanced method development, and fair performance evaluation.

eess.IV↗

arXiv2024

An Equilibrium Model for Schedule-Based Transit Networks with Hard Vehicle Capacities

Modelling passenger assignments in public transport networks is a fundamental task for city planners, especially when deliberating network infrastructure decisions. A key aspect of a realistic model is to integrate passengers' selfish routing behaviour under limited vehicle capacities. We formulate a side-constrained user equilibrium model in a schedule-based transit network, where passengers are modelled via a continuum of non-atomic agents that travel from their origin to their destination. An agent's route may comprise several rides along given lines, each using vehicles with hard loading capacities. We give a characterization of (side-constrained) user equilibria via a quasi-variational inequality and prove their existence for fixed departure times by generalizing a well-known result of Bernstein and Smith (Transp. Sci., 1994). We further derive a polynomial time algorithm for single-commodity instances with fixed departure times. For the multi-commodity case with departure time choice, we show that deciding whether an equilibrium exists is NP-hard, and we devise an exponential-time algorithm that computes an equilibrium if it exists, and signals non-existence otherwise. Using our quasi-variational characterization, we formulate a heuristic for computing multi-commodity user equilibria in practice, which is tested on multiple real-world instances. In terms of social cost, the computed user-equilibria are quite efficient compared to a system optimum.

cs.GT↗

arXiv2023

A deep learning approach to using wearable seismocardiography (SCG) for diagnosing aortic valve stenosis and predicting aortic hemodynamics obtained by 4D flow MRI

In this paper, we explored the use of deep learning for the prediction of aortic flow metrics obtained using 4D flow MRI using wearable seismocardiography (SCG) devices. 4D flow MRI provides a comprehensive assessment of cardiovascular hemodynamics, but it is costly and time-consuming. We hypothesized that deep learning could be used to identify pathological changes in blood flow, such as elevated peak systolic velocity Vmax in patients with heart valve diseases, from SCG signals. We also investigated the ability of this deep learning technique to differentiate between patients diagnosed with aortic valve stenosis (AS), non-AS patients with a bicuspid aortic valve (BAV), non-AS patients with a mechanical aortic valve (MAV), and healthy subjects with a normal tricuspid aortic valve (TAV). In a study of 77 subjects who underwent same-day 4D flow MRI and SCG, we found that the Vmax values obtained using deep learning and SCGs were in good agreement with those obtained by 4D flow MRI. Additionally, subjects with TAV, BAV, MAV, and AS could be classified with ROC-AUC values of 92%, 95%, 81%, and 83%, respectively. This suggests that SCG obtained using low-cost wearable electronics may be used as a supplement to 4D flow MRI exams or as a screening tool for aortic valve disease.

cs.LG↗

arXiv2022

MRI-MECH: Mechanics-informed MRI to estimate esophageal health

Dynamic magnetic resonance imaging (MRI) is a popular medical imaging technique to generate image sequences of the flow of a contrast material inside tissues and organs. However, its application to imaging bolus movement through the esophagus has only been demonstrated in few feasibility studies and is relatively unexplored. In this work, we present a computational framework called mechanics-informed MRI (MRI-MECH) that enhances that capability thereby increasing the applicability of dynamic MRI for diagnosing esophageal disorders. Pineapple juice was used as the swallowed contrast material for the dynamic MRI and the MRI image sequence was used as input to the MRI-MECH. The MRI-MECH modeled the esophagus as a flexible one-dimensional tube and the elastic tube walls followed a linear tube law. Flow through the esophagus was then governed by one-dimensional mass and momentum conservation equations. These equations were solved using a physics-informed neural network (PINN). The PINN minimized the difference between the measurements from the MRI and model predictions ensuring that the physics of the fluid flow problem was always followed. MRI-MECH calculated the fluid velocity and pressure during esophageal transit and estimated the mechanical health of the esophagus by calculating wall stiffness and active relaxation. Additionally, MRI-MECH predicted missing information about the lower esophageal sphincter during the emptying process, demonstrating its applicability to scenarios with missing data or poor image resolution. In addition to potentially improving clinical decisions based on quantitative estimates of the mechanical health of the esophagus, MRI-MECH can also be enhanced for application to other medical imaging modalities to enhance their functionality as well.

physics.med-ph↗

arXiv2021

Fluid-structure instability forecasts thoracic aortic aneurysm progression

The basic mechanism driving aneurysm growth is unknown. Currently, clinical diagnosis of an aneurysm is mainly informed by retrospective tracking of its size and growth rate. However, aneurysms can rupture before reactive criteria are met or remain stable when they are exceeded. Here, we identify a fluid-structure instability that is associated with abnormal aortic dilatation. Our analysis yields a measurable dimensionless number and its analytically derived critical threshold. This threshold pinpoints the transition from stable flow to unstable aortic fluttering as a function of the physiological properties composing the dimensionless number, like blood pressure and aortic compliance. A retrospective study was then conducted with 4D-flow MRI data from 117 patients indicated for cardiac imaging and 100 healthy volunteers recruited prospectively. The difference between the dimensionless number and its critical threshold was calculated for every subject from their earliest MRI data and used as an aneurysm physiomarker to forecast future growth. As a binary predictor for abnormal growth and subsequent surgical intervention reported from follow-up imaging, the aneurysm physiomarker yielded an AUC of 0.997 in a receiving operator characteristic analysis. Though validated here for thoracic ascending aortic aneurysms, this instability mechanism may be used to understand, predict and inform patient-specific treatment of aneurysms in any location without fundamental differences.

physics.med-ph↗

arXiv2021

Machine-Learned Prediction Equilibrium for Dynamic Traffic Assignment

We study a dynamic traffic assignment model, where agents base their instantaneous routing decisions on real-time delay predictions. We formulate a mathematically concise model and define dynamic prediction equilibrium (DPE) in which no agent can at any point during their journey improve their predicted travel time by switching to a different route. We demonstrate the versatility of our framework by showing that it subsumes the well-known full information and instantaneous information models, in addition to admitting further realistic predictors as special cases. We then proceed to derive properties of the predictors that ensure a dynamic prediction equilibrium exists. Additionally, we define $\varepsilon$-approximate DPE wherein no agent can improve their predicted travel time by more than $\varepsilon$ and provide further conditions of the predictors under which such an approximate equilibrium can be computed. Finally, we complement our theoretical analysis by an experimental study, in which we systematically compare the induced average travel times of different predictors, including two machine-learning based models trained on data gained from previously computed approximate equilibrium flows, both on synthetic and real world road networks.

cs.GT↗

arXiv2019

A Process Algebra for Link Layer Protocols

We propose a process algebra for link layer protocols, featuring a unique mechanism for modelling frame collisions. We also formalise suitable liveness properties for link layer protocols specified in this framework. To show applicability we model and analyse two versions of the Carrier-Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol. Our analysis confirms the hidden station problem for the version without virtual carrier sensing. However, we show that the version with virtual carrier sensing not only overcomes this problem, but also the exposed station problem with probability 1. Yet the protocol cannot guarantee packet delivery, not even with probability 1.

cs.NI↗

arXiv2019

4D-Flow MRI Pressure Estimation Using Velocity Measurement-Error based Weighted Least-Squares

This work introduces a 4D-flow magnetic resonance imaging (MRI) pressure reconstruction method which employs weighted least-squares (WLS) for pressure integration. Pressure gradients are calculated from the velocity fields, and velocity errors are estimated from the velocity divergence for incompressible flow. Pressure gradient errors are estimated by propagating the velocity errors through Navier-Stokes momentum equation. A weight matrix is generated based on the pressure gradient errors, then employed for pressure reconstruction. The pressure reconstruction method was demonstrated and analyzed using synthetic velocity fields as well as Poiseuille flow measured using in vitro 4D-flow MRI. Performance of the proposed WLS method was compared to the method of solving the pressure Poisson equation which has been the primary method used in the previous studies. Error analysis indicated that the proposed method is more robust to velocity measurement errors. Improvement on pressure results was found to be more significant for the cases with spatially-varying velocity error level, with reductions in error ranging from 50% to over 200%. Finally, the method was applied to flow in a patient-specific cerebral aneurysm. Validation was performed with in vitro flow data collected using Particle Tracking Velocimetry (PTV) and Shake the Box (STB) method, and in vivo flow measurement obtained using 4D-flow MRI. Pressure calculated by WLS, as opposed to the Poisson equation, was more consistent with the flow structures and showed better agreement between the in vivo and in vitro data. These results suggest the utility of WLS method to obtain reliable pressure field from clinical flow measurement data.

physics.flu-dyn↗

arXiv2019

Patient-Specific Cerebral Aneurysm Hemodynamics: Comparison of in vitro Volumetric Particle Velocimetry, Computational Fluid Dynamics (CFD), and in vivo 4D Flow MRI

Typical approaches to patient-specific hemodynamic studies of cerebral aneurysms use image based computational fluid dynamics (CFD) and seek to statistically correlate parameters such as wall shear stress (WSS) and oscillatory shear index (OSI) to risk of growth and rupture. However, such studies have reported contradictory results, emphasizing the need for in-depth comparisons of volumetric experiments and CFD. In this work, we conducted tomographic particle velocimetry experiments using two patient-specific cerebral aneurysm models (basilar tip and internal carotid artery) under pulsatile flow conditions and processed the particle images using Shake the Box (STB), a particle tracking method. The STB data was compared to that obtained from in vivo 4D flow MRI and CFD. Although qualitative agreement of flow pathlines across modalities was observed, each modality maintained notably unique spatiotemporal distributions of low normalized WSS regions. Analysis of time averaged WSS (TAWSS), OSI, and Relative Residence Time (RRT) demonstrated that non-dimensional parameters, such as OSI, may be more robust to the varying assumptions, limitations, and spatial resolutions of each subject and modality. These results suggest a need for further multi-modality analysis as well as development of non-dimensional hemodynamic parameters and correlation of such metrics to aneurysm risk of growth and rupture.

physics.flu-dyn↗